Method of measuring variation, inspection system, computer program, and computer system

ABSTRACT

Methods of measuring variation across multiple instances of a pattern on a substrate or substrates after a step in a device manufacturing process are disclosed. In one arrangement, data representing a set of images is received. Each image represents a different instance of the pattern, wherein the pattern includes a plurality of pattern elements. The set of images are registered relative to each other to superimpose the instances of the pattern. The registration includes applying different weightings to two or more of the plurality of pattern elements, wherein the weightings control the extent to which each pattern element contributes to the registration of the set of images and each weighting is based on an expected variation of the pattern element to which the weighting is applied. Variation in the pattern is measured using the registered set of images.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is the U.S. national phase entry of PCT patentapplication no. PCT/EP2018/053031, filed on Feb. 7, 2018, which claimsthe benefit of priority of European patent application no. 17157931.1which was filed on Feb. 24, 2017, and which is incorporated herein inits entirety by reference.

FIELD

The present invention relates to measuring variation between differentinstances of a pattern on a substrate or substrates, particularly in thecontext of lithography.

BACKGROUND

A lithographic apparatus is a machine that applies a desired patternonto a substrate, usually onto a target portion of the substrate. Alithographic apparatus can be used in one or more stages of a devicemanufacturing process, such as in the manufacture of integrated circuits(ICs). In that instance, a patterning device, which is alternativelyreferred to as a mask or a reticle, may be used to generate a circuitpattern to be formed on an individual layer of the IC. This pattern canbe transferred onto a target portion (e.g., comprising part of, one, orseveral dies) on a substrate (e.g., a silicon wafer). Transfer of thepattern is typically via imaging onto a layer of radiation-sensitivematerial (resist) provided on the substrate. In general, a singlesubstrate will contain a network of adjacent target portions that aresuccessively patterned. Known lithographic apparatus include so-calledsteppers, in which each target portion is irradiated by exposing anentire pattern onto the target portion at one time, and so-calledscanners, in which each target portion is irradiated by scanning thepattern through a radiation beam in a given direction (the“scanning”-direction) while synchronously scanning the substrateparallel or anti-parallel to this direction. It is also possible totransfer the pattern from the patterning device to the substrate byimprinting the pattern onto the substrate.

In order to monitor a device manufacturing process, parameters of thepatterned substrate (and therefore of any aspect of the devicemanufacturing process that affects the patterned substrate) aremeasured. Parameters may include features of pattern shapes (including1D and 2D shapes), for example critical dimension (typically linewidth)of developed photosensitive resist and/or etched product features.Parameters may include feature heights and/or feature pitches.Parameters may further include line edge roughness and line widthroughness. These measurements may be performed on a product substrateand/or on a dedicated metrology target. There are various techniques formaking measurements of the microscopic structures formed in lithographicprocesses, including the use of scanning electron microscopes (SEMs) andvarious specialized tools.

It is also desirable to monitor variation of parameters of the patternedsubstrate at different positions on the substrate and between differentsubstrates. Such variation can be monitored by comparing images ofmultiple instances of a pattern, for example a nominally identicalpattern, on the substrate or on different substrates. A set of suchimages are registered (aligned) relative to each other and deviationsbetween the different images can be identified and quantified.

Existing methods for assessing variation across multiple instances of apattern have been found to be unreliable.

SUMMARY

It is desirable to provide improved methods for measuring variationacross multiple instances of a pattern.

According to an aspect of the invention, there is provided a method ofmeasuring variation across multiple instances of a pattern on asubstrate or substrates after a step in a device manufacturing process,comprising: receiving data representing a set of images, each imagerepresenting a different instance of the pattern; registering the set ofimages relative to each other to superimpose the instances of thepattern; and measuring variation in the pattern using the registered setof images, wherein: the pattern comprises a plurality of patternelements and the registration of the set of images comprises applyingdifferent weightings to two or more of the plurality of patternelements, the weightings controlling the extent to which each patternelement contributes to the registration of the set of images; and eachweighting is based on an expected variation of the pattern element towhich the weighting is applied.

According to another aspect of the invention, there is provided a methodof measuring variation across multiple instances of a pattern on asubstrate or substrates after a step in a device manufacturing process,comprising: receiving data representing a set of images, each imagerepresenting a different instance of the pattern; registering the set ofimages relative to each other to superimpose the instances of thepattern; and measuring variation in the pattern using the registered setof images, wherein: each image in the received set of images isdelimited by a boundary box; the registration of the set of imagescomprises setting a common boundary box for the set of images based onan intersection between the boundary boxes of the received set ofimages; and the registration of the set of images is performed using allpixels within the common boundary box for each image.

According to another aspect of the invention, there is provided a methodof registering a pattern in one or more images, the pattern comprising aplurality of pattern elements, each pattern element having a weightingthat controls the extent to which the pattern element contributes to theregistration of the pattern, the method comprising: determining avariation in at least one pattern element using a model describing apatterning process for creating the pattern; and determining a weightingassociated with the at least one pattern element based on the determinedvariation in the pattern element.

According to another aspect of the invention, there is provided aninspection system for measuring variation across multiple instances of apattern on a substrate or substrates after a step in a devicemanufacturing process, comprising: an image acquisition deviceconfigured to perform an imaging operation on a substrate or pluralityof substrates to obtain a set of images, each image representing adifferent instance of the pattern; and a computer system configured to:register the set of images relative to each other to superimpose theinstances of the pattern; and measure variation in the pattern using theregistered set of images, wherein: the pattern comprises a plurality ofpattern elements and the registration of the set of images comprisesapplying different weightings to two or more of the plurality of patternelements, the weightings controlling the extent to which each patternelement contributes to the registration of the set of images; and eachweighting is based on an expected variation of the pattern element towhich the weighting is applied.

According to another aspect of the invention, there is provided aninspection system for measuring variation across multiple instances of apattern on a substrate or substrates after a step in a devicemanufacturing process, comprising: an image acquisition deviceconfigured to perform an imaging operation on a substrate or pluralityof substrates to obtain a set of images, each image representing adifferent instance of the pattern; and a computer system configured to:register the set of images relative to each other to superimpose theinstances of the pattern; and measure variation in the pattern using theregistered set of images, wherein: each image in the received set ofimages is delimited by a boundary box; the registration of the set ofimages comprises setting a common boundary box for the set of imagesbased on an intersection between the boundary boxes of the received setof images; and the registration of the set of images is performed usingall pixels within the common boundary box for each image.

According to another aspect of the invention, there is provided aninspection system for measuring variation across multiple instances of apattern on a substrate or substrates after a step in a devicemanufacturing process, comprising: an image acquisition deviceconfigured to perform an imaging operation on a substrate or pluralityof substrates to obtain a set of images, each image representing adifferent instance of the pattern; and a computer system configured toregister the pattern across the set of images, the pattern comprising aplurality of pattern elements, each pattern element having a weightingthat controls the extent to which the pattern element contributes to theregistration of the pattern, the registration comprising: determining avariation in at least one pattern element across the set of images usinga model describing a patterning process for creating the pattern; anddetermining a weighting associated with the at least one pattern elementbased on the determined variation in the pattern element.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described, by way of exampleonly, with reference to the accompanying schematic drawings in whichcorresponding reference symbols indicate corresponding parts, and inwhich:

FIG. 1 depicts a lithographic apparatus;

FIG. 2 depicts a lithographic cell or cluster;

FIGS. 3-4 depict inconsistent labeling of objects in different images;

FIGS. 5-6 depict inconsistent boundary boxes in different images;

FIGS. 7-8 depict inconsistent splitting of an object in differentimages;

FIGS. 9-10 depict inconsistent joining of separate objects in differentimages;

FIGS. 11-12 illustrate how apparent variations in objects can varyaccording to the choice of which objects to use for registration;

FIG. 13 depicts an iterative method of measuring variation betweennominally identical patterns;

FIGS. 14-15 depict example choices of different weightings for differentpattern elements;

FIGS. 16-17 depict stacking of a set of images registered according toan embodiment;

FIGS. 18-19 depict stacking of the set of images of FIGS. 16 and 17registered using the center of gravity of objects in the images;

FIG. 20 depicts derivation of a common boundary box using anintersection between boundary boxes of a set of images; and

FIG. 21 depicts an inspection system according to an embodiment.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

This specification discloses one or more embodiments that incorporatethe features of this invention. The disclosed embodiment(s) merelyexemplify the invention. The scope of the invention is not limited tothe disclosed embodiment(s). The invention is defined by the claimsappended hereto.

The embodiment(s) described, and references in the specification to “oneembodiment,” “an embodiment,” “an example embodiment,” etc., indicatethat the embodiment(s) described may include a particular feature,structure, or characteristic, but every embodiment may not necessarilyinclude the particular feature, structure, or characteristic. Moreover,such phrases are not necessarily referring to the same embodiment.Further, when a particular feature, structure, or characteristic isdescribed in connection with an embodiment, it is understood that it iswithin the knowledge of one skilled in the art to effect such feature,structure, or characteristic in connection with other embodimentswhether or not explicitly described.

Before describing such embodiments in more detail, however, it isinstructive to present an example environment in which embodiments ofthe present invention may be implemented.

FIG. 1 schematically depicts a lithographic apparatus LA. The apparatusincludes an illumination system (illuminator) IL configured to conditiona radiation beam B (e.g., UV radiation or DUV radiation), a supportstructure (e.g., a mask table) MT constructed to support a patterningdevice (e.g., a mask) MA and connected to a first positioner PMconfigured to accurately position the patterning device in accordancewith certain parameters, a substrate table (e.g., a wafer table) WTconstructed to hold a substrate (e.g., a resist coated wafer) W andconnected to a second positioner PW configured to accurately positionthe substrate in accordance with certain parameters, and a projectionsystem (e.g., a refractive projection lens system) PS configured toproject a pattern imparted to the radiation beam B by patterning deviceMA onto a target portion C (e.g., comprising one or more dies) of thesubstrate W.

The illumination system may include various types of optical components,such as refractive, reflective, magnetic, electromagnetic,electrostatic, or other types of optical components, or any combinationthereof, for directing, shaping, or controlling radiation.

The support structure supports, i.e., bears the weight of, thepatterning device. It holds the patterning device in a manner thatdepends on the orientation of the patterning device, the design of thelithographic apparatus, and other conditions, such as for examplewhether or not the patterning device is held in a vacuum environment.The support structure can use mechanical, vacuum, electrostatic or otherclamping techniques to hold the patterning device. The support structuremay be a frame or a table, for example, which may be fixed or movable asrequired. The support structure may ensure that the patterning device isat a desired position, for example with respect to the projectionsystem. Any use of the terms “reticle” or “mask” herein may beconsidered synonymous with the more general term “patterning device.”

The term “patterning device” used herein should be broadly interpretedas referring to any device that can be used to impart a radiation beamwith a pattern in its cross-section such as to create a pattern in atarget portion of the substrate. It should be noted that the patternimparted to the radiation beam may not exactly correspond to the desiredpattern in the target portion of the substrate, for example if thepattern includes phase-shifting features or so called assist features.Generally, the pattern imparted to the radiation beam will correspond toa particular functional layer in a device being created in the targetportion, such as an integrated circuit.

The patterning device may be transmissive or reflective. Examples ofpatterning devices include masks, programmable mirror arrays, andprogrammable LCD panels. Masks are well known in lithography, andinclude mask types such as binary, alternating phase-shift, andattenuated phase-shift, as well as various hybrid mask types. An exampleof a programmable mirror array employs a matrix arrangement of smallmirrors, each of which can be individually tilted so as to reflect anincoming radiation beam in different directions. The tilted mirrorsimpart a pattern in a radiation beam, which is reflected by the mirrormatrix.

The term “projection system” used herein should be broadly interpretedas encompassing various types of projection system, includingrefractive, reflective, catadioptric, magnetic, electromagnetic andelectrostatic optical systems, or any combination thereof, asappropriate for the exposure radiation being used, or for other factorssuch as the use of an immersion liquid or the use of a vacuum. Any useof the term “projection lens” herein may be considered as synonymouswith the more general term “projection system.”

In this embodiment, for example, the apparatus is of a transmissive type(e.g., employing a transmissive mask). Alternatively, the apparatus maybe of a reflective type (e.g., employing a programmable mirror array ofa type as referred to above, or employing a reflective mask).

The lithographic apparatus may be of a type having two (dual stage) ormore substrate tables and, for example, two or more mask tables. In such“multiple stage” machines the additional tables may be used in parallel,or preparatory steps may be carried out on one or more tables while oneor more other tables are being used for exposure.

The lithographic apparatus may also be of a type wherein at least aportion of the substrate may be covered by a liquid having a relativelyhigh refractive index, e.g., water, so as to fill a space between theprojection system and the substrate. An immersion liquid may also beapplied to other spaces in the lithographic apparatus, for examplebetween the mask and the projection system. Immersion techniques arewell known in the art for increasing the numerical aperture ofprojection systems. The term “immersion” as used herein does not meanthat a structure, such as a substrate, must be submerged in liquid, butrather only means that liquid is located between the projection systemand the substrate during exposure.

Referring to FIG. 1, the illuminator IL receives a radiation beam from aradiation source SO. The source and the lithographic apparatus may beseparate entities, for example when the source is an excimer laser. Insuch cases, the source is not considered to form part of thelithographic apparatus and the radiation beam is passed from the sourceSO to the illuminator IL with the aid of a beam delivery system BDcomprising, for example, suitable directing mirrors and/or a beamexpander. In other cases the source may be an integral part of thelithographic apparatus, for example when the source is a mercury lamp.The source SO and the illuminator IL, together with the beam deliverysystem BD if required, may be referred to as a radiation system.

The illuminator IL may comprise an adjuster AD for adjusting the angularintensity distribution of the radiation beam. Generally, at least theouter and/or inner radial extent (which are commonly referred to asG-outer and G-inner, respectively) of the intensity distribution in apupil plane of the illuminator can be adjusted. In addition, theilluminator IL may comprise various other components, such as anintegrator IN and a condenser CO. The illuminator may be used tocondition the radiation beam to have a desired uniformity and intensitydistribution in its cross section.

The radiation beam B is incident on the patterning device (e.g., maskMA), which is held on the support structure (e.g., mask table MT), andis patterned by the patterning device. Having traversed the mask MA, theradiation beam B passes through the projection system PS, which focusesthe beam onto a target portion C of the substrate W. With the aid of thesecond positioner PW and position sensor IF (e.g., an interferometricdevice, linear encoder, 2-D encoder or capacitive sensor), the substratetable WT can be moved accurately, e.g., so as to position differenttarget portions C in the path of the radiation beam B. Similarly, thefirst positioner PM and another position sensor (which is not explicitlydepicted in FIG. 1) can be used to accurately position the mask MA withrespect to the path of the radiation beam B, e.g., after mechanicalretrieval from a mask library, or during a scan. In general, movement ofthe mask table MT may be realized with the aid of a long-stroke module(coarse positioning) and a short-stroke module (fine positioning), whichform part of the first positioner PM. Similarly, movement of thesubstrate table WT may be realized using a long-stroke module and ashort-stroke module, which form part of the second positioner PW. In thecase of a stepper (as opposed to a scanner) the mask table MT may beconnected to a short-stroke actuator only, or may be fixed. Mask MA andsubstrate W may be aligned using mask alignment marks M1, M2 andsubstrate alignment marks P1, P2. Although the substrate alignment marksas illustrated occupy dedicated target portions, they may be located inspaces between target portions (these are known as scribe-lane alignmentmarks). Similarly, in situations in which more than one die is providedon the mask MA, the mask alignment marks may be located between thedies.

The depicted apparatus could be used in at least one of the followingmodes:

1. In step mode, the mask table MT and the substrate table WT are keptessentially stationary, while an entire pattern imparted to theradiation beam is projected onto a target portion C at one time (i.e., asingle static exposure). The substrate table WT is then shifted in the Xand/or Y direction so that a different target portion C can be exposed.In step mode, the maximum size of the exposure field limits the size ofthe target portion C imaged in a single static exposure.

2. In scan mode, the mask table MT and the substrate table WT arescanned synchronously while a pattern imparted to the radiation beam isprojected onto a target portion C (i.e., a single dynamic exposure). Thevelocity and direction of the substrate table WT relative to the masktable MT may be determined by the (de-)magnification and image reversalcharacteristics of the projection system PS. In scan mode, the maximumsize of the exposure field limits the width (in the non-scanningdirection) of the target portion in a single dynamic exposure, whereasthe length of the scanning motion determines the height (in the scanningdirection) of the target portion.

3. In another mode, the mask table MT is kept essentially stationaryholding a programmable patterning device, and the substrate table WT ismoved or scanned while a pattern imparted to the radiation beam isprojected onto a target portion C. In this mode, generally a pulsedradiation source is employed and the programmable patterning device isupdated as required after each movement of the substrate table WT or inbetween successive radiation pulses during a scan. This mode ofoperation can be readily applied to maskless lithography that utilizesprogrammable patterning device, such as a programmable mirror array of atype as referred to above.

Combinations and/or variations on the above described modes of use orentirely different modes of use may also be employed.

As shown in FIG. 2 the lithographic apparatus LA forms part of alithographic cell LC, also sometimes referred to as a lithocell orcluster, which also includes apparatus to perform pre- and post-exposureprocesses on a substrate. Conventionally these include spin coaters SCto deposit resist layers, developers DE to develop exposed resist, chillplates CH and bake plates BK. A substrate handler, or robot, RO picks upsubstrates from input/output ports I/O1, I/O2, moves them between thedifferent process apparatus and delivers then to the loading bay LB ofthe lithographic apparatus. These devices, which are often collectivelyreferred to as the track, are under the control of a track control unitTCU that is itself controlled by the supervisory control system SCS,which also controls the lithographic apparatus via lithography controlunit LACU. Thus, the different apparatus can be operated to maximizethroughput and processing efficiency.

In order that the substrates that are exposed by the lithographicapparatus are exposed correctly and consistently, it is desirable toinspect exposed substrates to measure properties such as overlay errorsbetween subsequent layers, line thicknesses, critical dimensions (CD),etc. If errors are detected, adjustments, for example, can be made toexposures of subsequent substrates, especially if the inspection can bedone soon and fast enough that other substrates of the same batch arestill to be exposed. Also, already exposed substrates may be strippedand reworked to improve yield, or possibly be discarded, therebyavoiding performing exposures on substrates that are known to be faulty.In a case where only some target portions of a substrate are faulty,further exposures can be performed only on those target portions thatare deemed to be non-faulty.

An inspection apparatus, which may also be referred to as a metrologyapparatus, is used to determine the properties of the substrates, and inparticular, how the properties of different substrates or differentlayers of the same substrate vary from layer to layer. The inspectionapparatus may be integrated into the lithographic apparatus LA or thelithocell LC or may be a stand-alone device. To enable most rapidmeasurements, it is desirable that the inspection apparatus measureproperties in the exposed resist layer immediately after the exposure.However, the latent image in the resist has a very low contrast, as inthere is only a very small difference in refractive index between theparts of the resist which have been exposed to radiation and those whichhave not—and not all inspection apparatus have sufficient sensitivity tomake useful measurements of the latent image. Therefore measurements maybe taken after the post-exposure bake step (PEB) that is customarily thefirst step carried out on exposed substrates and increases the contrastbetween exposed and unexposed parts of the resist. At this stage, theimage in the resist may be referred to as semi-latent. It is alsopossible to make measurements of the developed resist image, at whichpoint either the exposed or unexposed parts of the resist have beenremoved, or after a pattern transfer step such as etching. The latterpossibility limits the possibilities for rework of faulty substrates butmay still provide useful information.

It is desirable to measure variation across multiple instances of apattern, for example a set of nominally identical patterns, on the samesubstrate, or between different substrates, after a step in a devicemanufacturing process, for example a device manufacturing method thatincludes one or more lithographic steps. The multiple instances may bemeasured after any step in the device manufacturing process, includingsteps involving exposure of the substrate and other processing stepssuch as post-exposure bake, developing, and subsequent pattern formationsteps such as etching, chemical mechanical planarization (CMP), andfilling/deposition (e.g. using chemical vapor deposition, CVD). Themultiple instances may be formed at different positions on the samesubstrate, on different substrates, or a combination of both. Nominallyidentical patterns are patterns which would be identical (andidentically positioned) if the relevant steps of the devicemanufacturing process were error free. Nominally identical patterns willnormally comprise patterns that are formed at the same stage of alithographic process (e.g. before etching or after etching). Parameterswhich are of particular interest when measuring the variation includeline edge roughness and line width roughness, but other parameters mayalso be measured, including parameters related to placement of featuresin the pattern (e.g. differences between expected edge positions andmeasured edge positions). The measured variation provides informationabout errors in the device manufacturing process. This information canbe used to improve the device manufacturing process and thereby improvepatterning robustness.

Measuring variation involves comparing different instances of a pattern.The comparison typically comprises registering (aligning) differentinstances of the pattern relative to each other to computationallysuperimpose the different instances.

A known approach for implementing registration is to align differentimages based on calculating the center of gravity of a selected subsetof features in each image. The calculated centers of gravity are thenused to perform the registration (e.g. by aligning the centers ofgravity as closely as possible). This approach is computationallyefficient but prone to error. Examples of factors contributing to errorare discussed below with reference to FIGS. 3-12.

As illustrated in FIGS. 3 and 4, corresponding objects in differentimages may erroneously be given different IDs. In the simple casedepicted, an image comprises two objects 11 and 12 within a boundary box10. The objects 11 and 12 are, however, labelled differently in theimage of FIG. 3 in comparison with the image of FIG. 4. Such labellingerrors cause relatively large shifts in the apparent center of gravitiesof the objects affected even though the objects themselves may be stable(i.e. well aligned over the set of images being processed).

As illustrated in FIGS. 5 and 6, objects that are fully visible in oneimage may not be fully visible in all images being compared. In the casedepicted, objects 11 and 12 are fully visible in the image of FIG. 5 butonly object 12 is fully visible in the image of FIG. 6. The object 11near the edge of the boundary box 10 in FIG. 5 is partially cut-off bythe boundary box 10 in FIG. 6. The boundary box 10 in FIG. 6 isdisplaced relative to the boundary box 10 of FIG. 5 (depicted by abroken line in FIG. 6). Variation in the positioning of the boundary box10 (which may be defined for example by the field of view of the imageacquisition device used to obtain the image) relative to objects withinthe boundary box 10 may arise for example due to variations in theaccuracy of a stage used to support the substrate and/or due to errorsin pattern recognition algorithms used to identify the patterns to becompared. Variations in the extent to which objects are visible willlead to a corresponding variation in the positions of centers of gravityallocated to such objects even though the objects themselves may bestable.

As illustrated in FIGS. 7-10, variation in the lithographic process maycause objects to be erroneously split into multiple objects in a subsetof the images (FIGS. 7 and 8) or may cause plural objects to beerroneously joined together to form a single object in a subset of theimages (FIGS. 9 and 10). In the example shown in FIGS. 7 and 8, a singleobject 13 is present in the boundary box 10 of FIG. 7, but the sameobject is split into two separate objects 13A and 13B in the boundarybox 10 of FIG. 8. If the image of FIG. 7 is analyzed to determine acenter of gravity of the object 13, a single point will be determinedthat is located roughly in the neck region of the object 13. Bycontrast, if the image of FIG. 8 is analyzed to determine a center ofgravity, two distinct objects 13A and 13B will be identified, eachhaving its own center of gravity that is displaced significantlyrelative to the position of the center of gravity of the object 13 ofFIG. 7. Similar considerations apply to the example shown in FIGS. 9 and10, where two separate objects 14 and 15 (with two corresponding centersof gravity) are present in the image of FIG. 9 but are present as asingle object 16 (with a single center of gravity) in the image of FIG.10. Such splitting or joining of objects causes artificial shifts in thecenters of gravity involved, resulting in errors in the registration ofthe images.

A further source of error when using centers of gravity of selectedobjects is that some objects are more susceptible to variation betweendifferent images than other objects. This means that the choice of whichobjects to use for the registration procedure can have a significanteffect on the accuracy of the registration and, therefore, onmeasurements of variation in the pattern that rely on the registration.In particular, if an object having high variation is used for theregistration, variations in the position of this object may cause otherobjects to appear variable when they are in fact relatively stable. Thevariation in the object used for the registration is thus effectivelytransferred to other objects in the pattern. This effect is illustratedin FIGS. 11 and 12, which each show stacking of the same set of imagescontaining two objects 17 and 18 after registration. Three schematiccontour lines are shown for each object 17 and 18 to indicate relativevariation in the outer edge of each object. FIG. 11 depicts the casewhere the set of images are registered using the object 17 as an anchor(e.g. based on the center of gravity of the object 17). FIG. 12 depictsthe case where the set of images are registered using object 18 as theanchor. It can be seen that the choice of anchor has a marked effect onthe apparent variability of the two objects 17 and 18. In FIG. 11,apparent variation along the right hand side of object 18 in enhanced.In FIG. 12, apparent variation along the left hand side of object 17 isenhanced.

FIG. 13 is a flow chart depicting a method according to an embodimentwhich addresses the problems discussed above. The method measuresvariation across multiple instances of a pattern on a substrate orsubstrates after a step in a device manufacturing process. The multipleinstances of the pattern may comprise multiple instances of a nominallyidentical pattern. Alternatively or additionally, the multiple instancesof the pattern may comprise multiple instances of the pattern with adegree of deliberately added variation in the pattern. For example,variation in the pattern may be deliberately induced by varyingpatterning process parameters such as focus or dose. In this way themeasured variation may be used to evaluate pattern stability as afunction of patterning process parameters. For example, a focus and/ordose range over which variation in the pattern is measured to be withinan acceptable range may be used to determine best focus or best dosevalues or ranges. In an embodiment, the device manufacturing methodcomprises one or more lithographic steps.

In step S1, data representing a set of images is received. In theexample shown the data is received from a database 21. In otherembodiments the data is received directly from an image acquisitiondevice. The image data may be derived from measurements performed by ascanning electron microscope (SEM) for example. Each image represents adifferent instance of the pattern. The different instances correspond tothe pattern formed at different positions on a substrate and/or ondifferent substrates. The substrate or substrates may comprisesemiconductor wafers patterned by a semiconductor device manufacturingprocess.

The method comprises registering the set of images relative to eachother. The registration comprises aligning or superimposing (stacking)the images so that they can be compared to identify variations betweenthe different instances. In an embodiment, an initial coarseregistration may be performed in step S1 based on a standard patternmatching algorithm. The coarse registration may comprise alignment of anSEM image (or a binary version of the SEM image) relative to a data filedefining a mask pattern (e.g. GDSII). The coarse registration may beused to determine initial positions of boundary boxes of the images(e.g. the positions of the boundary boxes when the images are alignedwith each other) in order to determine a common boundary boxcorresponding to an intersection between the boundary boxes, asdescribed further below. In subsequent steps weightings can be used toimprove the registration. In the example of FIG. 13, furtherregistration steps comprise an iterative sequence including steps S2-S5.In other embodiments, the further registration may be performed withoutiteration.

The pattern, for example nominally identical pattern, comprises aplurality of pattern elements. In an embodiment, one or more of thepattern elements each comprises all or a portion of an edge defining anobject in the pattern. The object may be defined by an edge forming aclosed contour within the image (e.g. object 12 in FIG. 6), or by anedge forming an open contour within the image, not including theboundary box itself (e.g. due to the object overlapping with a boundarybox 10 of the image, as is the case for object 11 in FIG. 6).

In an embodiment, the registration of the images comprises applyingdifferent weightings to two or more of the plurality of patternelements. The different weightings may comprise discrete numericalvalues or a continuous weighting function. The weightings control theextent to which each pattern element contributes to the registration ofthe set of images. Each weighting is based on an expected variation ofthe pattern element to which the weighting is applied. In an embodiment,the weightings are such that pattern elements having relatively highexpected variation contribute less to the registration of the set ofimages than pattern elements having lower expected variation.

The weightings can be derived in an automated process, for example basedon physics principles or knowledge of pattern formation processes. In anembodiment, the expected variation of each pattern element is obtainedusing a model describing a patterning process for creating the pattern.The expected variation of each pattern element is used to obtain theweighting for that pattern element. For example, in an embodiment, themethod comprises determining a variation in at least one pattern elementusing the model and determining a weighting associated with the at leastone pattern element based on the determined variation in the patternelement. This registration process is used here in the context ofmeasuring variations of a pattern across a set of images but theregistration process may also be provided as a stand alone process. Inthis case the pattern may be registered in one or a set of images, forexample relative to a reference pattern.

The model may take into account physics principles or knowledge ofpattern formation processes. In an embodiment the expected variation ofeach pattern element is obtained by modeling the pattern element atdifferent patterning process parameters, for example under differentdose or focus conditions. In an embodiment, the model comprises a modelof a lithographic process.

The use of weightings makes it possible to reduce the extent to whichpattern elements of relatively high variability contribute to theregistration process and thereby cause errors in the registrationprocess. The use of weightings reduces or removes the need to manuallyintervene in the registration process, for example to manually excluderegions which are not suitable for registration. The use of weightingsalso makes it possible for pattern elements having low variability tocontribute more to the registration process than they otherwise would,thereby further reducing errors in the registration process. Reducingerrors in the registration process improves the accuracy of measurementsof variation in the nominally identical pattern. Detected variation ismore likely to be due to real variation than variation induced byerroneous registration of the images.

In the embodiment of FIG. 13, the weightings are generated and appliedto the pattern elements in step S2. Information about the expectedvariation of the pattern elements may be supplied by database 22.Alternatively or additionally, information about the expected variationmay be provided from measurements of the variation in the set of imagesthemselves via the NO branch of step S5. For example, in an embodiment,the first time step S2 is performed the weightings are set equal for allpattern elements. Step S3 then registers the set of images based on theequal weightings and a first measurement of variation is performed inthe following step S4. The method then follows the NO branch of step S5and the step S2 then uses the variation in the pattern measured in thepreceding step S4 to generate the first set of weightings to improve theregistration process.

In step S3, registration of the set of images relative to each other isperformed using the weightings generated and applied in step S2 (ifweightings are not set to be equal—see above). Various algorithms knownin the art of pattern matching may be used for the registration. In oneparticular embodiment, as described further below, cross-correlation isused to match each image to a common reference image. Examples of commonreference images are given below.

In step S4, variation in the pattern is measured over the set of images,as registered in step S3. Various metrics may be used to quantify thevariation. In one particular embodiment, a metric quantifying variationin transformation fields embodying determined transformations betweenthe images and a common reference image are used, as described furtherbelow.

In step S5, the output from step S4 is tested to determine whether theiterative process has converged to a satisfactory extent. This may beachieved for example by comparing the current output from step S4 with apreceding output from S4. If a difference between the outputs is largerthan a predetermined threshold, the method proceeds via the NO branch ofstep S5 to perform a further iteration (otherwise the method proceedsvia the YES branch). In such a further iteration, information aboutvariation in the set of images is used to refine the weightings appliedin step S2. For example, pattern elements which have been found in stepS4 to have relatively high variation may be down-weighted and/or patternelements which have been found in step S4 to have relatively lowvariation may be up-weighted. The process then continues until the YESbranch of step S5 is encountered and the method proceeds to step S6. Instep S6, the measured variation in the pattern is output.

The method of FIG. 13 is thus an example of an embodiment in which theregistering of the set of images comprises an iterative processinvolving at least a first registration step (the first time step S3 isperformed) followed by a second registration step (the next time step S3is performed, after following the NO branch of step S5). Each of thefirst registration step and the second registration step comprisesregistering the set of images relative to each other to superimpose theinstances of the pattern. At least the second registration stepcomprises applying different weightings to two or more pattern elements.One or more weightings used in the second registration step aregenerated using variation determined (in step S4 in this example) usingthe registration of the first registration step. The first registrationstep may or may not use different weightings for different patternelements.

Information about the expected variation of the pattern elements, assupplied for example via the database 22 in the method of FIG. 13, maybe obtained in various ways. It has been described above for example howthe expected variation may be obtained using a model describing apatterning process for creating the pattern. Further non-limitingexamples are given below, which may or may not involve use of such amodel.

In an embodiment, each of one or more of the weightings is generatedusing a simulated slope of an aerial image intensity (e.g. thenormalized image-log slope, NILS) of a lithographic process defining allor a portion of the pattern element. In an embodiment, the weightingvaries inversely as a function of the simulated slope of the aerialimage intensity. Pattern elements defined by edges having shallowerslopes are weighted lower (i.e. such that they contribute less toregistration) than pattern elements defined by edges having steeperslopes. Edges corresponding to shallower simulated slopes will beexpected to vary more across the set of images than edges correspondingto steeper simulated slopes and will therefore be less optimal forachieved accurate registration.

In an embodiment, each of one or more of the weightings is generatedbased on a nominal geometry (i.e. a geometry that would be formed ifrelevant preceding steps of the device manufacturing process were errorfree) of the pattern element. In an embodiment, the nominal geometry iscompared with a library containing different geometries and associatedexpected variabilities. The expected variabilities may be obtained fromcalibration measurements, simulations, or general knowledge in the fieldof lithographic processes. It is well known for example that certainclasses of geometry are more difficult to form accurately usinglithography than others.

In an embodiment, each of one or more of the weightings is generatedbased on a property of the pattern environment adjacent to the patternelement. For example, it is known that variation of an edge is likely tobe higher when the edge is located adjacent to an open space incomparison to when the edge is located adjacent to a denser region ofpattern. Thus, in an embodiment the pattern element forms part of anobject in the pattern and the property of the pattern environmentcomprises the length in a direction perpendicular to an edge of theobject in which no other object is present. The property of the patternenvironment may comprise a line separation for example in the case of a1D pattern of lines. The property of the pattern environment mayalternatively or additionally comprise a measure of the pattern densityadjacent to the pattern element. An approach to generating weightings ofthis type is illustrated in FIGS. 14 and 15. FIG. 14 depicts a patternwithin a bounding box 10. The pattern depicts three objects 21, 22 and23 consisting of parallel vertical lines. Object 21 is a relative thinline having an open area 31 on the left and a series of denser lines onthe right. The denser lines include objects 22 and 23 and are separatedfrom each other by smaller open areas 32. It is known that an object 21adjacent to an open area 31 will often be more difficult to formaccurately than objects 22 and 23 in denser regions because of a greatersensitivity to process variations. The greater sensitivity to processvariations may arise for example due to a lower aerial image contrast orslope of intensity. The object 21 will therefore be expected to have alarger variation across the set of images, particularly on the left handside of the object 21, than the other objects 22 and 23. This knowledgeof the expected variation can be used to choose weightings that improvethe registration process. FIG. 15 shows an example choice of weightings.A left half of the object 21 is given a relatively low weighting of 0.2.The right half of object 21 is given a higher weighting 0.7, reflectingthe fact that the objects 22 and 23 will tend to assist with accurateformation of the right hand side of object 21. Objects 22 and 23 aregiven still higher weightings of 0.9 and 1.0.

In an embodiment, each image in the received set of images is delimitedby a boundary box 10. The boundary box 10 may be defined for example byan imaging process (e.g. SEM) used to obtain the image (e.g. a field ofview of the imaging process) or by subsequent processing of the image.The boundary box may be defined by or equal to a field of view of theimaging process. In an embodiment, as depicted schematically in FIG. 20,the registration of the set of images comprises setting a commonboundary box 10′ for the set of images based on an intersection betweenthe boundary boxes 10 of the received set of images. In an embodiment,the common boundary box 10′ is equal to the intersection between theboundary boxes 10. In an embodiment, a coarse registration step of theimages is performed in order to define initial positions of the boundaryboxes 10 in order to calculate the intersection between the boundaryboxes. Setting a common boundary box, which is the same for all of theimages, improves accuracy of the registration process by reducing theextent to which variations in the boundary boxes of the set of imagescan be misinterpreted as variation in the pattern. The shape of theboundary box 10′ is not particularly limited, but may typically berectangular or square.

In an embodiment, the registration of the set of images is performedusing all pixels within the common boundary box for each image. Theproblems with prior art approaches that use only selected features ofeach image to perform the registration, for example to obtain centers ofgravity of closed objects as discussed above, are therefore reduced oravoided. In particular, the reduction in accuracy caused by performingregistration based on pattern elements with high variability arereduced. Using all of the pixels within the common boundary box for eachimage reduces the influence of pattern elements with high variability onthe final registration. The influence of such pattern elements may bereduced further by down-weighting such elements, as described above withreference to FIG. 13, but the advantages of using all of the pixelswithin the common boundary box for each image are achieved even withoutapplying weightings. Thus, in the case where the registration isperformed using all of the pixels within the common boundary box foreach image, methodology of the type depicted in FIG. 13 could beimplemented without steps S2 and S5.

In an embodiment, the registration of the set of images is performed byreference to a mathematical transformation of each image to a commonreference image. The registration may for example comprise minimizing amathematical transformation by varying a position of each image relativeto the common reference image until a best fit is obtained. In oneparticular class of embodiments the registration of the set of images isperformed using a cross-correlation in Fourier space. Thecross-correlation may be performed with an upsampledmatrix-multiplication discrete Fourier transform (DFT) to achievearbitrary subpixel precision. In a case where weightings are applied todifferent pattern elements in an image, the registration may for examplecomprise comparing a binary image (consisting of only {0,1}) with areference image containing weights per pixel as values in the range of[0,1].

In an embodiment, the measurement of variation comprises calculating avariation across the mathematical transformations for the set of images.In one example, each mathematical transformation is represented by avector field and may be referred to as a transformation field. Thetransformation field may comprise vectors joining each participatingpixel in the image to a corresponding pixel in the common referenceimage. Calculating variations in a transformation field can be achievedmore efficiently and consistently than prior art alternatives such ascharacterizing variation by reference to normals to an average contour.

In an embodiment, the common reference image comprises one or more ofthe following: a selected one of the set of images being processed, anintended pattern to be formed, or a mask pattern or image of alithographic process in the device manufacturing process. The intendedpattern to be formed may be defined by a data file such as a GDSII fileand may or may not contain optical proximity correction features.

FIGS. 16 and 17 depict registration of a set of 199 images according toan embodiment in which all pixels in a common boundary box for eachimage are used for the registration. FIGS. 18 and 19 depict registrationof the same 199 images using a standard center of gravity basedalignment. FIGS. 16 and 18 depict stacking of the registered set ofimages using a linear shading scale (from 1-199). FIGS. 17 and 19 depictthe same stacking but with a non-linear scaling which increases thevisibility of variations. The scaling represents a multiple of astandard deviation away from a mean. Thus, 0.0 corresponds to a meanvalue, 2.0 corresponds to twice a standard deviation greater than themean, and −2.0 corresponds to twice a standard deviation less than themean. The range of −2.0 to 2.0 shown thus covers about 95% of thecontours.

The stacking shown in FIGS. 16 and 18 appears similar but the non-linearscaling of FIGS. 17 and 19 reveals significant differences inperformance between the two approaches to registration. In particular,large differences between FIGS. 17 and 19 can be seen in the protrudingregion indicated by the large arrow. The variation is much larger inFIG. 19 than in FIG. 17. Furthermore, pattern elements which are morestable, such as the portion of the edge of the object indicated by thesmaller arrows, are seen to be registered significantly less well inFIG. 19 than in FIG. 17. The width of the edge, which is a measure ofapparent variation in this pattern element across the registered set ofimages, is significantly larger in FIG. 19 than in FIG. 17. Theincreased width is likely due to variations in regions such as thatindicated by the large arrow effectively transferring variation to othermore stable regions by reducing the accuracy of the registration processfor those regions.

The nature of each image in the set of images is not particularlylimited. In an embodiment, each image is a binary image. The binaryimage may be obtained for example using an edge detection algorithm.Binary images can be stored and processed efficiently.

FIG. 21 depicts an inspection system suitable for implementing themethod. The inspection system comprises an image acquisition device 40and a computer system 50. The image acquisition device 40 performs animaging operation on a substrate or plurality of substrates to obtainthe data representing a set of images. The data is provided to a datareceiving unit 51 of the computer system 50 and the subsequentprocessing steps are performed by a data processing unit 52. Computerhardware for implementing such functionality is well known in the art.

The embodiments may further be described using the following clauses:

1. A method of measuring variation across multiple instances of apattern on a substrate or substrates after a step in a devicemanufacturing process, comprising:

receiving data representing a set of images, each image representing adifferent instance of the pattern;

registering the set of images relative to each other to superimpose theinstances of the pattern; and

measuring variation in the pattern using the registered set of images,wherein:

the pattern comprises a plurality of pattern elements and theregistration of the set of images comprises applying differentweightings to two or more of the plurality of pattern elements, theweightings controlling the extent to which each pattern elementcontributes to the registration of the set of images;

2. The method of clause 1, wherein each weighting is based on anexpected variation of the pattern element to which the weighting isapplied.

3. The method of clause 1 or 2, wherein each pattern element comprisesall or a portion of an edge defining an object in the pattern.

4. The method of clause 2 or 3, wherein the weightings are such that apattern element having a relatively high expected variation willcontribute less to the registration of the set of images than a patternelement having a lower expected variation.

5. The method of any of clauses 2 to 4, wherein the expected variationof each pattern element is obtained using a model describing apatterning process for creating the pattern.

6. The method of clause 5, wherein the expected variation of eachpattern element is obtained by modeling the pattern element at differentpatterning process parameters.

7. The method of clause 5 or 6, wherein the model comprises a model of alithographic process.

8. The method of any preceding clause, wherein each of one or more ofthe weightings is generated using a simulated slope of an aerial imageintensity of a lithographic process defining all or a portion of thepattern element in the device manufacturing process.9. The method of any preceding clause, wherein each of one or more ofthe weightings is generated based on a nominal geometry of the patternelement.10. The method of any preceding clause, wherein each of one or more ofthe weightings is generated based on a property of the patternenvironment adjacent to the pattern element.11. The method of clause 10, wherein each pattern element forms part ofan object in the pattern and the property of the pattern environmentcomprises the length in a direction perpendicular to an edge of theobject in which no other object is present.12. The method of any preceding clause, wherein the registration of theset of images comprises an iterative process involving at least a firstregistration step followed by a second registration step, the firstregistration step and the second registration step each comprisingregistering the set of images relative to each other to superimpose theinstances of the pattern; wherein at least the second registration stepcomprises applying different weightings to two or more of the pluralityof pattern elements, the weightings controlling the extent to which eachpattern element contributes to the registration of the set of images inthe second registration step; and one or more of the weightings used inthe second registration step are generated using variation in thepattern determined using the registration of the first registrationstep.13. The method of any preceding clause, wherein each image in thereceived set of images is delimited by a boundary box;

the registration of the set of images comprises setting a commonboundary box for the set of images based on an intersection between theboundary boxes of the received set of images; and

the registration of the set of images is performed using all pixelswithin the common boundary box for each image.

14. A method of measuring variation across multiple instances of apattern on a substrate or substrates after a step in a devicemanufacturing process, comprising:

receiving data representing a set of images, each image representing adifferent instance of the pattern;

registering the set of images relative to each other to superimpose theinstances of the pattern; and

measuring variation in the pattern using the registered set of images,wherein:

each image in the received set of images is delimited by a boundary box;

the registration of the set of images comprises setting a commonboundary box for the set of images based on an intersection between theboundary boxes of the received set of images.

15. the method of clause 14, wherein the registration of the set ofimages is performed using all pixels within the common boundary box foreach image.

16. The method of clause 13 or 14, wherein the common boundary box issquare or rectangular.

17. The method of any preceding clause, wherein the registration of theset of images comprises determining a mathematical transformation ofeach image to a common reference image.

18. The method of clause 17, wherein the measurement of variationcomprises calculating a variation across the determined mathematicaltransformations for the set of images.

19. The method of clause 17 or 18, wherein the common reference imagecomprises one or more of the following: a selected one of the set ofimages, an intended pattern to be formed, or a mask pattern of alithographic process in the device manufacturing process.20. The method of any preceding clause, wherein each image in the set ofimages comprises a binary image.21. The method of any preceding clause, wherein the multiple instancesof a pattern comprise multiple instances of a nominally identicalpattern.22. The method of any preceding clause, wherein the device manufacturingprocess comprises one or more lithographic steps.23. A method of registering a pattern in one or more images, the patterncomprising a plurality of pattern elements, each pattern element havinga weighting that controls the extent to which the pattern elementcontributes to the registration of the pattern, the method comprising:

determining a variation in at least one pattern element using a modeldescribing a patterning process for creating the pattern; and

determining a weighting associated with the at least one pattern elementbased on the determined variation in the pattern element.

24. The method of clause 23, wherein the determining of the variation inthe at least one pattern element comprises modelling the at least onepattern element at different patterning process parameters.

25. The method of clause 23 or 24, wherein the model comprises a modelof a lithographic process.

26. The method of any preceding clause, wherein one or more of theimages comprises a scanning electron microscope image of the pattern ona semiconductor wafer produced in a device manufacturing process.

27. An inspection system for measuring variation across multipleinstances of a pattern on a substrate or substrates after a step in adevice manufacturing process, comprising:

an image acquisition device configured to perform an imaging operationon a substrate or plurality of substrates to obtain a set of images,each image representing a different instance of the pattern; and

a computer system configured to:

register the set of images relative to each other to superimpose theinstances of the pattern; and

measure variation in the pattern using the registered set of images,wherein:

the pattern comprises a plurality of pattern elements and theregistration of the set of images comprises applying differentweightings to two or more of the plurality of pattern elements, theweightings controlling the extent to which each pattern elementcontributes to the registration of the set of images.

28. The inspection system of clause 27, wherein each weighting is basedon an expected variation of the pattern element to which the weightingis applied.

29. An inspection system for measuring variation across multipleinstances of a pattern on a substrate or substrates after a step in adevice manufacturing process, comprising:

an image acquisition device configured to perform an imaging operationon a substrate or plurality of substrates to obtain a set of images,each image representing a different instance of the pattern; and

a computer system configured to:

register the set of images relative to each other to superimpose theinstances of the pattern; and measure variation in the pattern using theregistered set of images, wherein:

each image in the received set of images is delimited by a boundary box;

the registration of the set of images comprises setting a commonboundary box for the set of images based on an intersection between theboundary boxes of the received set of images.

30. The inspection system of clause 29, wherein the registration of theset of images is performed using all pixels within the common boundarybox for each image.

31. An inspection system for measuring variation across multipleinstances of a pattern on a substrate or substrates after a step in adevice manufacturing process, comprising:

an image acquisition device configured to perform an imaging operationon a substrate or plurality of substrates to obtain a set of images,each image representing a different instance of the pattern; and

a computer system configured to register the pattern across the set ofimages, the pattern comprising a plurality of pattern elements, eachpattern element having a weighting that controls the extent to which thepattern element contributes to the registration of the pattern, theregistration comprising:

determining a variation in at least one pattern element across the setof images using a model describing a patterning process for creating thepattern; and

determining a weighting associated with the at least one pattern elementbased on the determined variation in the pattern element.

32. A computer program comprising computer-readable instructions that,when executed by a computer system, cause the computer system to performthe method of any of clauses 1 to 26.

33. A computer system configured to perform the method of any of clauses1 to 26.

Although specific reference may be made in this text to the use oflithographic apparatus in the manufacture of ICs, it should beunderstood that the lithographic apparatus described herein may haveother applications, such as the manufacture of integrated opticalsystems, guidance and detection patterns for magnetic domain memories,flat-panel displays, liquid-crystal displays (LCDs), thin film magneticheads, etc. The skilled artisan will appreciate that, in the context ofsuch alternative applications, any use of the terms “wafer” or “die”herein may be considered as synonymous with the more general terms“substrate” or “target portion”, respectively. The substrate referred toherein may be processed, before or after exposure, in for example atrack (a tool that typically applies a layer of resist to a substrateand develops the exposed resist), a metrology tool and/or an inspectiontool. Where applicable, the disclosure herein may be applied to such andother substrate processing tools. Further, the substrate may beprocessed more than once, for example in order to create a multi-layerIC, so that the term substrate used herein may also refer to a substratethat already contains multiple processed layers.

Although specific reference may have been made above to the use ofembodiments of the invention in the context of optical lithography, itwill be appreciated that the invention may be used in otherapplications, for example imprint lithography, and where the contextallows, is not limited to optical lithography. In imprint lithography atopography in a patterning device defines the pattern created on asubstrate. The topography of the patterning device may be pressed into alayer of resist supplied to the substrate whereupon the resist is curedby applying electromagnetic radiation, heat, pressure or a combinationthereof. The patterning device is moved out of the resist leaving apattern in it after the resist is cured.

The terms “radiation” and “beam” used herein encompass all types ofelectromagnetic radiation, including ultraviolet (UV) radiation (e.g.,having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) andextreme ultra-violet (EUV) radiation (e.g., having a wavelength in therange of 5-20 nm), soft X-ray, as well as particle beams, such as ionbeams or electron beams.

The term “lens,” where the context allows, may refer to any one orcombination of various types of optical components, includingrefractive, reflective, magnetic, electromagnetic, and electrostaticoptical components.

The foregoing description of the specific embodiments will so fullyreveal the general nature of the invention that others can, by applyingknowledge within the skill of the art, readily modify and/or adapt forvarious applications such specific embodiments, without undueexperimentation, without departing from the general concept of thepresent invention. Therefore, such adaptations and modifications areintended to be within the meaning and range of equivalents of thedisclosed embodiments, based on the teaching and guidance presentedherein. It is to be understood that the phraseology or terminologyherein is for the purpose of description and not of limitation, suchthat the terminology or phraseology of the present specification is tobe interpreted by the skilled artisan in light of the teachings andguidance.

The breadth and scope of the present invention should not be limited byany of the above-described exemplary embodiments, but should be definedonly in accordance with the following claims and their equivalents.

The invention claimed is:
 1. A method of measuring variation acrossmultiple instances of a pattern on a substrate or substrates after astep in a device manufacturing process, the method comprising: receivingdata representing a set of images, each image representing a differentinstance of the pattern; registering the set of images relative to eachother to superimpose the instances of the pattern; and measuringvariation in the pattern using the registered set of images, wherein:the pattern comprises a plurality of pattern elements and theregistration of the set of images comprises applying a differentweighting to each of two or more of the plurality of pattern elements,each of the weightings controlling the extent to which each respectivepattern element contributes to the registration of the set of images,and each weighting is based on an expected variation of the patternelement to which the weighting is applied.
 2. The method of claim 1,wherein each pattern element comprises all or a portion of an edgedefining an object in the pattern.
 3. The method of claim 1, wherein theweightings are such that a pattern element having a relatively highexpected variation will contribute less to the registration of the setof images than a pattern element having a lower expected variation. 4.The method of claim 1, wherein the expected variation of each patternelement is obtained using a model describing a patterning process forcreating the pattern.
 5. The method of claim 4, wherein the expectedvariation of each pattern element is obtained by modelling the patternelement at different patterning process parameters.
 6. The method ofclaim 4, wherein the model comprises a model of a lithographic process.7. The method of claim 1, wherein each of one or more of the weightingsis generated using a simulated slope of an aerial image intensity of alithographic process defining all or a portion of the pattern element inthe device manufacturing process.
 8. The method of claim 1, wherein eachof one or more of the weightings is generated based on a nominalgeometry of the pattern element.
 9. The method of claim 1, wherein eachof one or more of the weightings is generated based on a property of thepattern environment adjacent to the pattern element.
 10. The method ofclaim 9, wherein each pattern element forms part of an object in thepattern and the property of the pattern environment comprises the lengthin a direction perpendicular to an edge of the object in which no otherobject is present.
 11. The method of claim 1, wherein: the registrationof the set of images comprises an iterative process involving at least afirst registration step followed by a second registration step, thefirst registration step and the second registration step each comprisingregistering the set of images relative to each other to superimpose theinstances of the pattern; wherein at least the second registration stepcomprises applying a different weighting to each of two or more of theplurality of pattern elements, each of the weightings controlling theextent to which each respective pattern element contributes to theregistration of the set of images in the second registration step, andone or more of the weightings used in the second registration step aregenerated using variation in the pattern determined using theregistration of the first registration step.
 12. The method of claim 1,wherein: each image in the received set of images is delimited by aboundary box; the registration of the set of images comprises setting acommon boundary box for the set of images based on an intersectionbetween the boundary boxes of the received set of images; and theregistration of the set of images is performed using all pixels withinthe common boundary box for each image.
 13. The method of claim 1,wherein the registration of the set of images comprises determining amathematical transformation of each image to a common reference image.14. An inspection system, comprising: an image acquisition deviceconfigured to perform an imaging operation on a substrate or pluralityof substrates to obtain a set of images, each image representing adifferent instance of a pattern after a step in a device manufacturingprocess; and a computer system configured to at least: register the setof images relative to each other to superimpose the instances of thepattern; and measure variation in the pattern using the registered setof images, wherein: the pattern comprises a plurality of patternelements and the registration of the set of images comprises applicationof a different weighting to each of two or more of the plurality ofpattern elements, each of the weightings controlling the extent to whicheach respective pattern element contributes to the registration of theset of images, and each weighting is based on an expected variation ofthe pattern element to which the weighting is applied.
 15. Anon-transitory computer-readable program product comprisingcomputer-readable instructions therein, the instructions, upon executionby a computer system, configured to cause the computer system to atleast: receive data representing a set of images, each imagerepresenting a different instance of a pattern on a substrate orsubstrates after a step in a device manufacturing process; register theset of images relative to each other to superimpose the instances of thepattern; and measure variation in the pattern using the registered setof images, wherein: the pattern comprises a plurality of patternelements and the registration of the set of images comprises applying adifferent weighting to each of two or more of the plurality of patternelements, each of the weightings controlling the extent to which eachrespective pattern element contributes to the registration of the set ofimages, and each weighting is based on an expected variation of thepattern element to which the weighting is applied.
 16. Thecomputer-readable program product of claim 15, wherein the weightingsare such that a pattern element having a relatively high expectedvariation will contribute less to the registration of the set of imagesthan a pattern element having a lower expected variation.
 17. Thecomputer-readable program product of claim 15, wherein the instructionsare further configured to cause the computer system to determine theexpected variation of each pattern element using a model describing apatterning process for creating the pattern.
 18. The computer-readableprogram product of claim 15, wherein the instructions are furtherconfigured to cause the computer system to generate each of one or moreof the weightings using a simulated slope of an aerial image intensityof a lithographic process defining all or a portion of the patternelement in the device manufacturing process.
 19. The computer-readableprogram product of claim 15, wherein the instructions are furtherconfigured to cause the computer system to generate each of one or moreof the weightings based on a property of the pattern environmentadjacent to the pattern element.
 20. The computer-readable programproduct of claim 15, wherein: the registration of the set of imagescomprises at least a first registration followed by a secondregistration, the first registration and the second registration eachcomprising registration of the set of images relative to each other tosuperimpose the instances of the pattern; wherein at least the secondregistration comprises application of a different weighting to each oftwo or more of the plurality of pattern elements, each of the weightingscontrolling the extent to which each respective pattern elementcontributes to the registration of the set of images in the secondregistration, and one or more of the weightings used in the secondregistration are generated using variation in the pattern determinedusing the registration of the first registration.
 21. Thecomputer-readable program product of claim 15, wherein: each image inthe received set of images is delimited by a boundary box; theregistration of the set of images comprises setting of a common boundarybox for the set of images based on an intersection between the boundaryboxes of the received set of images; and the registration of the set ofimages is performed using all pixels within the common boundary box foreach image.